Theory of membrane capacitive deionization including the effect of the electrode pore space

Membrane capacitive deionization (MCDI) is a technology for water desalination based on applying an electrical field between two oppositely placed porous electrodes. Ions are removed from the water flowing through a channel in between the electrodes and are stored inside the electrodes. Ion-exchange membranes are placed in front of the electrodes allowing for counterion transfer from the channel into the electrode, while retaining the coions inside the electrode structure. We set up an extended theory for MCDI which includes in the description for the porous electrodes not only the electrostatic double layers (EDLs) formed inside the porous (carbon) particles, but also incorporates the role of the transport pathways in the electrode, i.e., the interparticle pore space. Because in MCDI the coions are inhibited from leaving the electrode region, the interparticle porosity becomes available as a reservoir to store salt, thereby increasing the total salt storage capacity of the porous electrode. A second advantage of MCDI is that during ion desorption (ion release) the voltage can be reversed. In that case the interparticle porosity can be depleted of counterions, thereby increasing the salt uptake capacity and rate in the next cycle. In this work, we compare both experimentally and theoretically adsorption/desorption cycles of MCDI for desorption at zero voltage as well as for reversed voltage, and compare with results for CDI. To describe the EDL-structure a novel modified Donnan model is proposed valid for small pores relative to the Debye length.